The nucleus of an atom is the central part containing protons and neutrons, while a nuclide is a specific type of atomic nucleus characterised by its number of protons and neutrons. In essence, a nucleus is a broader term referring to the core of an atom, whereas a nuclide is a more specific term referring to a particular kind of nucleus based on its composition.
An electron is a fundamental particle found within the atom's structure, while a beta particle is a high-energy electron or positron emitted during radioactive decay. While they are essentially the same particle (a negatively charged electron), they differ in their origin and the process by which they are produced.